Bisognano-Wichmann property for rigid categorical extensions and non-local extensions of conformal nets

Published 23 Dec 2019 in math-ph, math.MP, math.OA, and math.QA | (1912.10682v3)

Abstract: Given an (irreducible) Mobius covariant net $\mathcal A$, we prove a Bisognano-Wichmann theorem for its categorical extension $\mathscr E^{{\textrm{d}}$} associated to the braided $C^*$-tensor category $\textrm{Rep}^{{\textrm{d}}(\mathcal} A)$ of dualizable (more precisely "dualized") Mobius covariant $\mathcal A$-modules. As a closely related result, we prove a (modified) Bisognano-Wichmann theorem for any (possibly) non-local extension of $\mathcal A$ obtained by a $C^*$-Frobenius algebra $Q$ in $\textrm{Rep}^{{\textrm{d}}(\mathcal} A)$. As an application, we discuss the relation between the domains of modular operators and the preclosedness of certain unbounded operators in $\mathscr E^{{\textrm{d}}$.}